Campus Units

Aerospace Engineering

Document Type

Article

Publication Version

Published Version

Publication Date

9-1992

Journal or Book Title

Journal of Applied Mechanics

Volume

59

First Page

604

Last Page

614

DOI

10.1115/1.2893766

Abstract

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.

Comments

This article is from Journal of Applied Mechanics 59 (1992): 604, doi: 10.1115/1.2893766. Posted with permission.

Copyright Owner

The American Society of Mechanical Engineers

Language

en

File Format

application/pdf

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